Right query to get the current number of connections in a PostgreSQL DB

Question

Which of the following two is more accurate?

select numbackends from pg_stat_database;

select count(*) from pg_stat_activity;

Answer 1

Aggregation of all postgres sessions per their status (how many are idle, how many doing something...)

select state, count(*) from pg_stat_activity  where pid <> pg_backend_pid() group by 1 order by 1;